Equation of Locus

Geometry Level 2

Find the equation of the locus of the center of a circle which moves so that it is tangent to the y y -axis and to a unit circle with center at ( 2 , 0 ) (2 , 0) .

y 2 − 6 x + 3 = 0 y^2-6x+3=0 2 x 2 + y 2 − 6 x + 3 = 0 2x^2+y^2-6x+3=0 x 2 + y 2 − 6 x + 3 = 0 x^2+y^2-6x+3=0 x 2 − 6 x + 3 = 0 x^2-6x+3=0

Pao Pao Cantos by Pao Pao Cantos , 28, Philippines

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1 solution

Andrea Coppola
Aug 14, 2016

Fast way: observe that the locus must include the circle centered in x=1/2 y=0, so you can exclude all the other suggested possible solutions

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